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A hypersurface x(M) in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists σ,a conformal transformation of R41,such that σ(x(M)) =x(M),σ(x(p)) =x(q).In this paper,the authors give a complete classification for regular time-like conformal homogeneous hypersurfaces in R41 with three distinct principal curvatures.